Kinetic analysis of p53 gene network with time delays and PIDD

p53 kinetics plays a key role in regulating cell fate. Based on the p53 gene regulatory network composed by the core regulatory factors ATM, Mdm2, Wip1, and PIDD, the effect of the delays in the process of transcription and translation of Mdm2 and Wip1 on the dynamics of p53 is studied theoretically and numerically. The results show that these two time delays can affect the stability of the positive equilibrium. With the increase of delays, the dynamics of p53 presents an oscillating state. Further, we also study the effects of PIDD and chemotherapeutic drug etoposide on the kinetics of p53. The model indicates that (i) PIDD low-level expression does not significantly affect p53 oscillatory behavior, but high-level expression could induce two-phase kinetics of p53; (ii) Too high and too low concentration of etoposide is not conducive to p53 oscillation. These results are in good agreement with experimental findings. Finally, we consider the influence of internal noise on the system through Binomial t-leap algorithm. Stochastic simulations reveal that high-intensity noise completely destroys p53 dynamics in the deterministic model, whereas low-intensity noise does not alter p53 dynamics. Interestingly, for the stable focus, the internal noise with appropriate intensity can induce quasi-limit cycle oscillations of the system. Our work may provide the useful insights for the development of anticancer therapy.